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A191416
E.g.f. 1/(1-sin(x))^x
0
1, 0, 2, 3, 16, 70, 360, 2212, 14488, 106272, 846530, 7287896, 67550052, 669276452, 7062219710, 79046250480, 935246925616, 11662366603504, 152856287604594, 2100714749805472, 30205647605518900
OFFSET
0,3
FORMULA
a(n):=2*n!*sum(m=1..n, sum(j=m..n/2, (stirling1(n-2*j+m,m)*(-1)^(n-2*j)*sum(i=0..(n+m)/2-j, (2*i+2*j-n-m)^(n-m)*binomial(n-2*j+m,i)*(-1)^(n-j-i)))/(2^(n-2*j+m)*(n-2*j+m)!))/(n-m)!), n>0, a(0)=1.
a(n) ~ n! * n^(Pi-1)*2^(n+3*Pi/2)/(Gamma(Pi)*Pi^(n+Pi)) * (1 - Pi*(Pi-1)*log(n)/n). - Vaclav Kotesovec, Jun 27 2013
MATHEMATICA
CoefficientList[Series[(1/(1-Sin[x]))^x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)
PROG
(Maxima)
a(n):=2*n!*sum( sum((stirling1(n-2*j+m, m)*(-1)^(n-2*j)*sum((2*i+2*j-n-m)^(n-m)*binomial(n-2*j+m, i)*(-1)^(n-j-i), i, 0, (n+m)/2-j))/(2^(n-2*j+m)*(n-2*j+m)!), j, m, n/2)/(n-m)!, m, 1, n);
CROSSREFS
Sequence in context: A052506 A355229 A052858 * A209004 A329121 A368765
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Jun 01 2011
STATUS
approved